# Branching Particle Pricers with Heston Examples

## TL;DR

This paper evaluates sequential Monte Carlo methods, especially particle branching algorithms, for efficient path-dependent option pricing under the Heston model, demonstrating significant performance improvements over other resampling techniques.

## Contribution

It introduces and advocates for the effective particle branching algorithm within importance-sampling Monte Carlo methods for improved path-dependent option pricing.

## Key findings

- Particle branching algorithms outperform resampling in certain cases.
- Explicit solutions and importance sampling enhance simulation efficiency.
- Numerical comparisons validate the recommended approach.

## Abstract

The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and volatility, especially for purposes of path-dependent option pricing. The resulting simulation algorithm is an analog to the weighted particle filtering algorithm that might be improved by resampling or branching. Indeed, some branching algorithms are shown herein to improve pricing performance substantially while some resampling algorithms are shown to be less suitable in certain cases. A historical property is given and explained as the distinguishing feature between the sequential Monte Carlo algorithms that work on path-dependent option pricing and those that do not. In particular, it is recommended to use the so-called effective particle branching algorithm within importance-sampling Monte Carlo methods for path-dependent option pricing. All recommendations are based upon numeric comparison of option pricing problems in the Heston model.